yes, I use their ferries every week. You can leave from St Martin Marigot or from St Martin Oyster Pond (40 minutes) to St Barths.
From Anguilla, you can take the ferry to St Martin Marigot (25 minutes) and use the Voyager ferry from Marigot to St Barths (they leave 5 days a week from Marigot; ask their schedule)